3. Presentation of the code and innovative parts
3.3 Code
3.3.3 Improvements and innovations
The most important innovations apported to the code are:
Production Rate variable also defined on the energy set e
Differentiation of electricity considering its sources.
Implementation of hydrogen pipeline as transportation mode.
Rewriting of Transportation Capital Cost equation.
Implementation of pipeline transportation in the Transportation Operating Cost
Implementation of hydrogen from abroad countries.
Rewriting of Global Warming Potential equations.
Rewriting of Facility operating cost equation.
However, before showing new equations and parameters, the overall superstructure and supply chain scheme used in this study must be explained.
In the study the superstructure type 5 (Fig.13 chapter 2) will be considered, being the most complete and flexible. This means that the code can select the optimal configuration by varying between a fully centralized, fully decentralized, or a solution with variable degree of decentralization. As already said, superstructures only report the general scheme of Hydrogen Supply Chain, without the definition of the technologies that can be used. For this reason, in Fig.14 is reported a different representation, presenting additional information such technologies that can be selected by the optimization tool and the energy sources.
38
Figure 14: General scheme of HSC
In this study the superstructure will be constituted by six echelons: primary energy source, hydrogen production, conditioning and centralized storage, transmission between grids, conditioning and decentralized storage, final usage.
After this clarifying introduction, the new equations and their parameters can be shown.
Production Rate variable also defined on the energy set e
In order to correctly evaluate costs and emissions, the variable Production Rate of product form 𝑖 produced by plant type 𝑝 and size 𝑗 in grid 𝑔 at the period 𝑡 (𝑃𝑅 , , , , , , 𝑖𝑛 ) is defined also on the energy set 𝑒, since there are multiple types of electricity that can power the electrolysers.
Differentiation of electricity considering its sources
In order to make a more accurate study, electricity was classified looking at its source:
𝑅𝐸𝑆: electricity produced from renewable sources directly coupled to the electrolysers.
𝐺𝑟𝑖𝑑 − 𝑒𝑙𝑒𝑐: electricity coming from the national network.
𝐺𝑟𝑖𝑑 − 𝑔𝑟𝑒𝑒𝑛: electricity coming from the national network, which is certified to be produced from renewable sources. In this case the renewable plant is not in the same location of the hydrogen production plant.
Implementation of hydrogen pipeline as transportation mode
The new transport method is added in the set of transport modes under the name 𝑝𝑖𝑝𝑒𝑙𝑖𝑛𝑒. The hydrogen mass flow balance remains unchanged, so it is taken as is from De Leon Almaraz [27]. However, a new equation must be written for the calculation of the Number of Transport Units (𝑁𝑇𝑈𝑔𝑟𝑖𝑑), since transport by pipeline is completely different from transport by road. For this reason, two subsets of the transport mode set 𝑙 have been introduced: road transport𝑙𝑟 and transport via pipeline 𝑙p. This escamotage allows to keep unchanged the 𝑁𝑇𝑈 equation treated previously and create a new one for pipelines (Eq. (13)). The new 𝑁𝑇𝑈𝑔𝑟𝑖𝑑 calculates the number of pipelines that must be installed between grid g and g’ at period t by
39
dividing the mass flow rate flowing into them (𝑄 , , , , 𝑖𝑛 ) for the maximum allowable flow rate in pipelines (𝑄𝑚𝑎𝑥 , 𝑖𝑛 ). In addition, this value is summed with 𝐸𝑝𝑠𝑖𝑙𝑜𝑛 , , , , , which yields integer values for the NTU variable. The 𝐸𝑝𝑠𝑖𝑙𝑜𝑛 equation is not present below because it was already considered in De Leon Almaraz [27].
𝑁𝑇𝑈𝑔𝑟𝑖𝑑 , , , , =𝑄 , , , ,
𝑄𝑚𝑎𝑥 , + 𝐸𝑝𝑠𝑖𝑙𝑜𝑛 , , , , ∀ 𝑔, 𝑔 , 𝑡 (13) With pipeline 𝑁𝑇𝑈, equations for CAPEX (Eq. (14) - Eq. (15)) and OPEX (Eq. (16)) for this new transportation method can be written. The Pipeline capital costs (𝑃𝐿𝐶𝐶 𝑖𝑛 €) for the first period is evaluated multiplying the Unit PipeLine Capital Cost parameter (𝑈𝑃𝐿𝐶𝐶 𝑖𝑛 €) for the average distance between different grids (𝐴𝐷 , 𝑖𝑛 𝑘𝑚) and the new 𝑁𝑇𝑈 (𝑁𝑇𝑈𝑔𝑟𝑖𝑑 , , , , ).
𝑃𝐿𝐶𝐶 = 𝑈𝑃𝐿𝐶𝐶 ∗ 𝐴𝐷 , ∗ 𝑁𝑇𝑈𝑔𝑟𝑖𝑑 , , , ,
, ,
(14)
However, for later periods, the capital costs for already installed pipelines should not be considered again, so in Eq. (15) there is the difference between 𝑁𝑇𝑈𝑔𝑟𝑖𝑑 variable at period t and 𝑁𝑇𝑈𝑔𝑟𝑖𝑑 at the previous period, avoiding considering the pipeline cost twice.
𝑃𝐿𝐶𝐶 = 𝑈𝑃𝐿𝐶𝐶 ∗ 𝐴𝐷 , ∗ (𝑁𝑇𝑈𝑔𝑟𝑖𝑑 , , , , − 𝑁𝑇𝑈𝑔𝑟𝑖𝑑 , , , , )
, ,
(15)
Finally, Eq. (16) allows to calculate the PipeLine Operational and maintenance Costs (𝑃𝐿𝑂𝐶 𝑖𝑛 € ). In the first part the parameter Unit PipeLine Operational Cost (𝑈𝑃𝐿𝑂𝐶 𝑖𝑛 € ) is multiplied with the mass flow rate flowing in pipelines (𝑄 , , , , 𝑖𝑛 ), representing the operational cost. The second part instead multiplies the PipeLine Capital Cost (𝑃𝐿𝐶𝐶 𝑖𝑛 €) for the maintenance cost as percentage of the capital cost, representing the maintenance costs (𝑑𝑒𝑙𝑡𝑎 𝑖𝑛 %). The two parts are summed together so:
𝑃𝐿𝑂𝐶 = 𝑈𝑃𝐿𝑂𝐶 ∗ 𝑄 , , ,
,
+ 𝑑𝑒𝑙𝑡𝑎 ∗ 𝑃𝐿𝐶𝐶(𝑡) (16)
Rewriting of Transportation Capital Cost equation
During the study, it was observed that the Transportation Capital Cost (𝑇𝐶𝐶 𝑖𝑛 €) equation used in De Leon Almaraz [27] incorrectly considers all vehicles present in each period, not considering those already present.
To overcome this problem the variable 𝑁𝑒𝑤𝑇𝑈, , is used, implemented with Eq. (17) and Eq. (18). The former simply does a summation over all possible combinations of 𝑔 and 𝑔 of 𝑁𝑇𝑈𝑔𝑟𝑖𝑑, , , , , evaluating the total number of transport systems for each physical form of hydrogen in the first period. Eq. (18), on the other hand, is used when the period is different from the first one, and makes the difference between the total number of transport units in the considered period (𝑁𝑇𝑈𝑔𝑟𝑖𝑑, , , , ) and the new transportation unit installed the previous period (𝑁𝑒𝑤𝑇𝑈, , ).
𝑁𝑒𝑤𝑇𝑈, , = 𝑁𝑇𝑈𝑔𝑟𝑖𝑑, , , ,
,
∀ 𝑖, 𝑙 (17)
𝑁𝑒𝑤𝑇𝑈, , = 𝑁𝑇𝑈𝑔𝑟𝑖𝑑, , , , − 𝑁𝑒𝑤𝑇𝑈, , ,
∀ 𝑖 , 𝑡 ≠ 1 (18)
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Moreover, in De Leon Almaraz [27] pipeline was not considered, so a new equation is used for 𝑇𝐶𝐶 calculation. Therefore in Eq. (19) is made the summation between the product of 𝑁𝑒𝑤𝑇𝑈, , for the Cost of establishing transportation mode 𝑇𝑀𝐶, 𝑖𝑛 € , and the PipeLine Capital Cost of the installed pipeline in the same period (𝑃𝐿𝐶𝐶(𝑡)).
𝑇𝐶𝐶 = 𝑁𝑒𝑤𝑇𝑈, , ∗ 𝑇𝑀𝐶, ,
+ 𝑃𝐿𝐶𝐶 ∀ 𝑡 (19)
Implementation of pipeline transportation in the Transportation Operating Cost
Due to the presence of a new transportation method, Transportation Operation Cost (𝑇𝑂𝐶 𝑖𝑛 € ) equation has to be modified. 𝑃𝐿𝑂𝐶 has to be added to the road transportation operating cost (Fuel Cost, General Cost, Labor Cost, Maintenance Cost) already defined in De Leon Almaraz [27].
𝑇𝑂𝐶 = 𝑃𝐿𝑂𝐶 + 𝐹𝐶 + 𝐺𝐶 + 𝐿𝐶 + 𝑀𝐶 ∀ 𝑡 (20) Implementation of hydrogen from abroad countries
Another brick that has been implemented in the code is the possibility to buy hydrogen from foreign Countries. This Hydrogen, generally named as “H2 coming from abroad” is considered as an energy source, therefore is inserted in the energy source type set 𝑒 as "ℎ𝑦𝑑𝑟𝑜𝑔𝑒𝑛”. Even if the production of this hydrogen takes place outside the system, it is necessary to add a new plant type called 𝑎𝑏𝑟𝑜𝑎𝑑 in order to respect the mass balance and the equations written in De Leon Almaraz [27]. Being introduced in the energy set 𝑒 and production set 𝑝, new equations are not needed.
Rewriting of Global Warming Potential equations
In De Leon Almaraz [27] and the other articles reviewed, the GWP calculation was already present, but with some limitations. In this study a new approach is followed, dividing the 𝐶𝑂 emission related to each HSC block, as done for the costs, into two parts:
- Installation emissions: emissions during the production and installation phases, related to the number of systems added in the considered period 𝑡;
- Operational emissions: emissions during the operational phase, related to the amount of hydrogen produced, stored, transported and delivered to the end users.
In this way emissions related to the number of installed systems are accounted, avoiding installing an unfeasible number of systems.
Production
For the production stage, Eq. (21) and Eq. (22) are implemented. The former evaluates emissions during the installation (𝑃𝐺𝑊𝑃𝑟𝑜𝑑 𝑖𝑛 𝑔 − 𝑒𝑞) as the summation of product between the number of installed production systems type 𝑝 size 𝑗 producing hydrogen in form 𝑖 (𝐼𝑃, , , , ) and the installation global warming potential of the plant type 𝑝 and size 𝑗 (𝐿𝐶𝐴 , 𝑖𝑛 ).
𝑃𝐺𝑊𝑃𝑟𝑜𝑑 = (𝐿𝐶𝐴 , 𝐼𝑃, , , ,
,
)
,
∀ 𝑡 (21)
With Eq. (22) instead is evaluate the production operating emission, related to the consumption of raw materials and energies (𝑃𝐺𝑊𝑃𝑟𝑜𝑑 𝑖𝑛 ). In the first summation, emissions during the production phase are evaluated as the products between the Production Rate of the plant type 𝑝 and size 𝑗 using the energy source 𝑒 (𝑃𝑅 , , , , , , ), the Energy Source Global Warming Potential of energy source 𝑒
41
used in the plant 𝑝 (𝐺𝑊𝐸𝑛𝑆𝑜𝑢𝑟𝑐𝑒 , 𝑖𝑛 𝑜𝑟 𝑜𝑟 ) and the rate of utilization of energy source 𝑒 by plant type 𝑝 and size 𝑗 (𝑔𝑎𝑚𝑎 , , 𝑖𝑛 𝑜𝑟 𝑜𝑟 ). The second summation instead accounts for the emission related to the compression of hydrogen in decentralized plants, in order to store it at a common pressure. In this last summation it is present the product between the Production Rate of the plant type 𝑝, 𝑜𝑛 − 𝑠𝑖𝑡𝑒 size and 𝑐𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑒𝑑 ℎ𝑦𝑑𝑟𝑜𝑔𝑒𝑛 (𝐶𝐻2) form (𝑃𝑅 , , , , , , ), the Specific Electricity Consumption of hydrogen compressor for 𝐶𝐻2 and compression rate similar to the one of the centralized plant (𝑆𝐸𝐶 , 𝑖𝑛
_ ) and the Energy Source Global Warming Potential of the
energy source 𝐺𝑟𝑖𝑑 − 𝑒𝑙𝑒𝑐 (𝐺𝑊𝐸𝑛𝑆𝑜𝑢𝑟𝑐𝑒 , ).
𝑃𝐺𝑊𝑃𝑟𝑜𝑑
= 𝑃𝑅 , , , , , , ∗ 𝐺𝑊𝐸𝑛𝑆𝑜𝑢𝑟𝑐𝑒𝑑 , ∗ 𝑔𝑎𝑚𝑎 , ,
, , , , ,
+ 𝑃𝑅, , , , , , ∗ 𝑆𝐸𝐶 , ∗ 𝐺𝑊𝐸𝑛𝑆𝑜𝑢𝑟𝑐𝑒𝑑 ,
, , ,
∀ 𝑡 (22)
Storage
As anticipated earlier, the formulation of the equations is similar across supply chain blocks. For centralized storage section Eq. (23) and Eq. (24) are used. The first one is quite similar to Eq. (21) and represents storage installation emissions (𝑆𝐺𝑊𝑆𝑡𝑜𝑐𝑘 𝑖𝑛 𝑔 − 𝑒𝑞) as the product between the number of Installed Storage systems of type𝑠 size𝑗 storing hydrogen in form 𝑖 (𝐼𝑆, , , , ) and the installation global warming potential of the storage type 𝑠 and size 𝑗 (𝐿𝐶𝐴 , 𝑖𝑛 ).
𝑆𝐺𝑊𝑆𝑡𝑜𝑐𝑘 = (𝐿𝐶𝐴 , 𝐼𝑆, , , ,
,
)
,
∀ 𝑡 (23)
The second equation instead evaluate the operating emissions (𝑆𝐺𝑊𝑆𝑡𝑜𝑐𝑘 𝑖𝑛 ) as summation of the product between the hydrogen stored, evaluated as the Total average inventory of product form 𝑖 in grid 𝑔 at the period 𝑡 (𝑆𝑇, , 𝑖𝑛 𝑘𝑔 ) divided by the Storage holding period in days 𝑏𝑒𝑡𝑎, the Specific Electricity Consumption for the hydrogen compression/liquefaction process (𝑆𝐸𝐶, ) for hydrogen form 𝑖 and size 𝑐𝑒𝑛𝑡𝑟𝑎𝑙𝑖𝑧𝑒𝑑 and the Energy Source Global Warming Potential of the energy source 𝐺𝑟𝑖𝑑 − 𝑒𝑙𝑒𝑐 (𝐺𝑊𝐸𝑛𝑆𝑜𝑢𝑟𝑐𝑒 , ), that represents emissions due to the consumption of electricity coming from the national network.
𝑆𝐺𝑊𝑆𝑡𝑜𝑐𝑘 = 𝑆𝑇, ,
𝑏𝑒𝑡𝑎 ∗ 𝑆𝐸𝐶, ∗𝐺𝑊𝐸𝑛𝑆𝑜𝑢𝑟𝑐𝑒𝐸𝑙𝑒𝑐𝑡𝑟𝑜𝑙𝑦𝑠𝑖𝑠,𝑔𝑟𝑖𝑑−𝑒𝑙𝑒𝑐 ,
∀ 𝑡 (24)
Transportation
Emissions from the transportation block are calculated using Eq. (25), Eq. (26) and Eq. (27). The first two equations evaluate the installation emissions (𝑇𝐺𝑊𝑇𝑟𝑎𝑛𝑠𝑝𝑜𝑟𝑡𝑎𝑡𝑖𝑜𝑛 𝑖𝑛 𝑔 − 𝑒𝑞) and take a cue from transportation costs formulations. Eq. (25) focuses on the first period, when no transportation means are already installed. In this equation road and pipeline emissions are tackle separately: in the first summation the product between the Number of New Transport Units for road transportation 𝑙𝑟 hydrogen form 𝑖 (𝑁𝑒𝑤𝑇𝑈, , ) and Installation Global warming potential of road transportation (𝐿𝐶𝐴 𝑖𝑛 ) is done; instead in the second summation, pipeline installation emission are calculated as the product between the distances between grids (𝐴𝐷 , ), the number of installed pipelines
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(𝑁𝑇𝑈𝑔𝑟𝑖𝑑 , , , , ) and the Installation Global warming potential of pipeline transportation
(𝐿𝐶𝐴 𝑖𝑛 ).
𝑇𝐺𝑊𝑇𝑟𝑎𝑛𝑠𝑝𝑜𝑟𝑡𝑎𝑡𝑖𝑜𝑛
= 𝑁𝑒𝑤𝑇𝑈, , ∗ 𝐿𝐶𝐴
,
+ 𝐴𝐷 , ∗ 𝑁𝑇𝑈𝑔𝑟𝑖𝑑 , , , , ∗ 𝐿𝐶𝐴
, ,
∀ 𝑡 (25)
For later periods, Eq. (26) should be used. For road transport the equation does not change, because is used the parameter 𝑁𝑒𝑤𝑇𝑈, , , which already accounts only transport methods installed in the considered period. For pipeline transport instead the summation is done on the product between the distances between grids (𝐴𝐷 , ), the Installation Global warming potential of pipeline transportation (𝐿𝐶𝐴 ) and the difference between the number of transportation unit in the considered period (𝑁𝑇𝑈𝑔𝑟𝑖𝑑, , , , ) and the new transportation unit installed the previous period (𝑁𝑒𝑤𝑇𝑈, , ).
𝑇𝐺𝑊𝑇𝑟𝑎𝑛𝑠𝑝𝑜𝑟𝑡𝑎𝑡𝑖𝑜𝑛
= 𝑁𝑒𝑤𝑇𝑈, , ∗ 𝐿𝐶𝐴
,
+ 𝐴𝐷 , ∗ (𝑁𝑇𝑈𝑔𝑟𝑖𝑑 , , , , − 𝑁𝑇𝑈𝑔𝑟𝑖𝑑 , , , , )
, ,
∗ 𝐿𝐶𝐴 ∀𝑡 (26) Operating emissions (𝑇𝐺𝑊𝑇𝑟𝑎𝑛𝑠𝑝𝑜𝑟𝑡𝑎𝑡𝑖𝑜𝑛 𝑖𝑛 ) instead are calculated with Eq. (27).
Also in this case the first summation is related to the road transportation, that is not explained here because is taken as it is from De Leon Almaraz [27], while the second one is added in this study in order to account pipeline operating emissions as summation of the product between hydrogen flow rate in pipes (𝑄 , , , ), Specific Electricity Consumption of hydrogen compressor for 𝐶𝐻2 and compression rate similar to the one of the centralized plant (𝑆𝐸𝐶 , ) and emissions due to the consumption of electricity coming from the national network.
(𝐺𝑊𝑃𝑟𝑜𝑑 , ).
𝑇𝐺𝑊𝑇𝑟𝑎𝑛𝑠𝑝𝑜𝑟𝑡𝑎𝑡𝑖𝑜𝑛
= 2 ∗ 𝐴𝐷 , ∗ 𝑄, , , ,
𝑇𝐶𝑎𝑝, ∗ 𝐺𝑊𝑇𝑟𝑎𝑛𝑠 ∗ 𝑤
, , ,
+ 𝑄 , , , , ∗ 𝑆𝐸𝐶 , ∗ 𝐺𝑊𝐸𝑛𝑆𝑜𝑢𝑟𝑐𝑒 ,
, ,
∀𝑡 (27)
Fueling station
Finally, the refueling station emissions are evaluated using Eq. (28) and Eq. (29). The first one evaluates the installation emissions as summation of the product between the number of Installed Fueling Stations of type 𝑓 and size 𝑗 dispensing hydrogen required form 𝑘 (𝐼𝐹𝑆, , , , ) and the installation global warming potential of the refueling station type 𝑓 and size 𝑗 (𝐿𝐶𝐴 , 𝑖𝑛 ).
𝐹𝐺𝑊𝑆𝑢𝑝𝑝𝑙𝑦 = 𝐼𝐹𝑆 , , , , ∗ 𝐿𝐶𝐴 ,
, , ,
∀ 𝑡 (28)
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Eq. (29), on the other hand, is used to calculate the operating emissions of fueling stations. In this equation, summation of the product between Hydrogen Total daily demand for mobility sector 𝑀𝑂𝐵 in grid 𝑔 (𝐷𝑇 , , 𝑖𝑛 ), the Specific Electricity Consumption for 𝑜𝑛 − 𝑠𝑖𝑡𝑒 hydrogen compressors (𝑆𝐸𝐶 , ) and the emissions related to the electricity consumption from the national network
(𝐺𝑊𝐸𝑛𝑆𝑜𝑢𝑟𝑐𝑒 , ) is performed.
𝐹𝐺𝑊𝑆𝑢𝑝𝑝𝑙𝑦 ,
= 𝐷𝑇 , , ∗ 𝑆𝐸𝐶 , ∗
,
𝐺𝑊𝐸𝑛𝑆𝑜𝑢𝑟𝑐𝑒 , ∀ 𝑡 (29)
Final Equations
Once all the Hydrogen Supply Chain blocks are considered, general equations should be used in order to sum together installation and operating emissions. For this reason, Eq. (30), Eq. (31), Eq. (32) and Eq. (34) are implemented. The former evaluates the yearly average GWP at the period𝑡 (𝐺𝑊𝑃𝑇𝑜𝑡 𝑖𝑛 ) as the sum between the operating emissions of each HSC section multiplied by the working days in a year (𝑊𝐷 𝑖𝑛 𝑑𝑎𝑦𝑠) and the installation emissions of each HSC section divided by the number of years in each period (in the case study equal to 5). In this way installation emissions, specific of the year of construction, are equally distributed over the years of same periods, while the operating emissions are calculated on an annual basis, allowing the two types of emissions to be added together.
𝐺𝑊𝑃𝑇𝑜𝑡 = 𝑃𝐺𝑊𝑃𝑟𝑜𝑑 + 𝑆𝐺𝑊𝑆𝑡𝑜𝑐𝑘 + 𝑇𝐺𝑊𝑇𝑟𝑎𝑛𝑠𝑝𝑜𝑟𝑡𝑎𝑡𝑖𝑜𝑛
+ 𝐹𝐺𝑊𝑆𝑢𝑝𝑝𝑙𝑦 , ∗ 𝑊𝐷 + (𝑃𝐺𝑊𝑃𝑟𝑜𝑑 + 𝑆𝐺𝑊𝑆𝑡𝑜𝑐𝑘
+ 𝑇𝐺𝑊𝑇𝑟𝑎𝑛𝑠𝑝𝑜𝑟𝑡𝑎𝑡𝑖𝑜𝑛 + 𝐹𝐺𝑊𝑆𝑢𝑝𝑝𝑙𝑦 )/5 ∀ 𝑡 (30) Moreover, knowing the overall GHG emissions for each period, emissions at the final user per unit hydrogen can be calculated, has reported in Eq. (31). Therefore, the Yearly average 𝐶𝑂 emissions of hydrogen in the period 𝑡 (𝑒𝑚𝑖𝑠𝑠𝑖𝑜𝑛 𝑖𝑛 ) is calculated as the ratio between 𝐺𝑊𝑃𝑇𝑜𝑡 and the total yearly hydrogen demand, calculated as the summation of the hydrogen daily demand for sector 𝑘 (𝐷𝑇, , ) multiplied for 𝑊𝐷.
𝑒𝑚𝑖𝑠𝑠𝑖𝑜𝑛 = 𝐺𝑊𝑃𝑇𝑜𝑡
𝑊𝐷 ∗ ∑ , 𝐷𝑇, , ∀ 𝑡 (31) Lastly, can be done the summation of all the GHG emissions in each periods (𝐺𝑊𝑃𝑇𝑜𝑡 ), finding the Total Global Warming Potential of HSC (𝐺𝑊𝑃𝑇𝑜𝑡𝑎𝑙 𝑖𝑛 𝑔 − 𝑒𝑞, Eq. (32)) and the final GHG emissions per kg of H2 produced and supplied (𝐻 𝑒𝑚𝑖𝑠𝑠𝑖𝑜𝑛 𝑖𝑛 , Eq. (33)), as the ratio between 𝐺𝑊𝑃𝑇𝑜𝑡𝑎𝑙 and the total hydrogen demand in the whole considered period.
𝐺𝑊𝑃𝑇𝑜𝑡𝑎𝑙 = 𝑃𝐺𝑊𝑃𝑟𝑜𝑑 + 𝑆𝐺𝑊𝑆𝑡𝑜𝑐𝑘 + 𝑇𝐺𝑊𝑇𝑟𝑎𝑛𝑠𝑝𝑜𝑟𝑡𝑎𝑡𝑖𝑜𝑛
+ 𝐹𝐺𝑊𝑆𝑢𝑝𝑝𝑙𝑦 , ∗ 𝑊𝐷 ∗ 5
+ 𝑃𝐺𝑊𝑃𝑟𝑜𝑑 + 𝑆𝐺𝑊𝑆𝑡𝑜𝑐𝑘 + 𝑇𝐺𝑊𝑇𝑟𝑎𝑛𝑠𝑝𝑜𝑟𝑡𝑎𝑡𝑖𝑜𝑛
+ 𝐹𝐺𝑊𝑆𝑢𝑝𝑝𝑙𝑦 (32)
𝐻 𝑒𝑚𝑖𝑠𝑠𝑖𝑜𝑛 = 𝐺𝑊𝑃𝑇𝑜𝑡𝑎𝑙
𝑊𝐷 ∗ 5 ∗ ∑ , , 𝐷𝑇, , (33)
44 Rewriting of Facility operating cost equation
In order to also account for the operating costs of refueling station, similar approach used in Luise et al. [30]
was considered, making some variations on the Facility Operating Cost (𝐹𝑂𝐶 𝑖𝑛 € ) equation. In particular, the formulation can be divided in three components. The first one related to the production, obtained as the products between Unit Production Cost of production plant type 𝑝, size 𝑐𝑒𝑛𝑡𝑟𝑎𝑙𝑖𝑧𝑒𝑑 producing hydrogen in form 𝑖 (𝑈𝑃𝐶 , , 𝑖𝑛 € ) and the Production Rate 𝑃𝑅 , , , , , , . The second one associated to the storage, calculated as the product of the Unit Storage Cost of storage type 𝑠, size𝑐𝑒𝑛𝑡𝑟𝑎𝑙𝑖𝑧𝑒𝑑 storing hydrogen in form 𝑖 (𝑈𝑆𝐶 , , 𝑖𝑛 ∗€ ) and the Total average inventory of hydrogen in form 𝑖 in grid 𝑔 (𝑆𝑇, , 𝑖𝑛 𝑘𝑔). The last element of the 𝐹𝑂𝐶 is the one related to the refueling stations: this member is composed of two parts that allow the separate evaluation of operational and maintenance costs. First, its operating costs are calculated as the products between the Hydrogen Total daily demand for sector 𝑘 in grid 𝑔 (𝐷𝑇𝑖𝑙, , , , 𝑖𝑛 ) and the Unit Fueling Station dispensing Cost of hydrogen form 𝑖 transported by transportation mean 𝑙 for sector 𝑘 (𝑈𝐹𝑆𝐶, , ). Then, the refueling stations maintenance costs are calculated as products of Number of Fueling Station of size 𝑗, 𝑀𝑂𝐵 sector (𝑁𝐹𝑆, , , , ), Fueling Station Capital Cost of station size 𝑗 and 𝑀𝑂𝐵 sector (𝐹𝑆𝐶𝐶, , 𝑖𝑛 €) and the variable 𝑑𝑒𝑙𝑡𝑎: this value is than divided by 𝑊𝐷 obtaing a cost per unit day, consistent with the other members of 𝐹𝑂𝐶. The 𝐼𝑁𝐷 sector is not considered in the above equation because hydrogen consumption systems are already in place at the considered industrial sites, therefore both capital and operating costs are fully covered by themself.
All this formulation is implemented in GAMS with Eq. (34).
𝐹𝑂𝐶 = ∑, ∑ , , , 𝑈𝑃𝐶 , , ∗ 𝑃𝑅 , , , , , , + ∑ 𝑈𝑆𝐶 , , ∗ 𝑆𝑇, , + ∑ , 𝐷𝑇𝑖𝑙, , , , ∗ 𝑈𝐹𝑆𝐶, , + ∑ , , 𝑁𝐹𝑆, , , , ∗ 𝐹𝑆𝐶𝐶, , ∗ 𝑊𝐷 ∗ 𝑑𝑒𝑙𝑡𝑎 ∀ 𝑡 (34)